Crabbing cavities are one of the technological landmark that will allow the LHC to optimize its per-formance and maximize its integrated luminosity by allowing a head-on collision between the bunches despite the non-zero crossing angle. A total of 8 crab cavities will be installed in the interaction region of each of the two experiments, ATLAS and CMS. In the last years, the two types of crab cavities were de-signed, built and tested under the US-LARP R&D pro-gram. Horizontal crabbing is obtained with a radio-frequency dipole cavity (RFD) designed by Old Do-minion University (ODU), SLAC and Fermilab (FNAL). In this paper a new mechanical design, that uses passive stiffeners, is presented. This design leads to a decrease of the Lorentz Force Detuning frequency shift, satisfy the requirements on pressure sensitivity, validate the structural integrity and increase the tuner sensitivity and the maximum elastic tuning range. Furthermore, it will be possible to greatly simplify the shape of the magnetic shield and Helium vessel with respect to the current design.